The number of solution(s) of the system of equations x+y=2π3 and cosx+cosy=32, where x and y are real, is
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Solution
We have cosx+cosy=32 ⇒2cos(x+y2)cos(x−y2)=32 ⇒2cosπ3cos(x−y2)=32(using:x+y=2π3) ⇒cos(x−y2)=32, which is not possible.
Hence, the system of equaitons has no solution.